Snowden is an American computer professional who leaked classified information from the National Security Agency (NSA), starting in June 2013. He has been a subject of controversy as his leaked documents revealed numerous global surveillance programmes, said the Hollywood Reporter.
Woodley, 22, would star opposite Joseph Gordon-Levitt, who is tackling the NSA whistleblower in the film, which will be distributed by Open Road in the US, said The Hollywood Reporter.
The 'Divergent' actress is poised to play the role of Snowden's girlfriend.
Stone is producing the untitled film with longtime producing partner Moritz Borman. The project is currently in preproduction in Germany with principal photography set to start in January.